How to detect a liar using a classic math trick

When trying to understand why people behave the way they do, we usually look to psychology. Studying how the human mind works is important for explaining actions and decisions. However, to truly describe how behavior evolves over time, psychology alone may not be enough. Adding mathematical thinking can reveal patterns and structures that are not obvious at first glance. By combining logic and numbers with psychological insight, we can better understand how people change their views and make choices.

The Science Behind Decision-Making

A recent model, published in Frontiers in Psychology, draws inspiration from the ideas of Norbert Wiener, a mathematician from the 19th century. This model examines how our opinions shift when we are faced with multiple choices. Often these changes occur because we must make decisions with limited information, analyzing what we know before choosing an option that shapes our behavior.

To better understand these patterns, researchers apply the mathematics of information processing. In a way, the human mind can be compared to a system that evaluates possibilities and assigns a probability to each one—whether it’s deciding which product to purchase, which school a child should attend, or which political candidate to support.

As we gather new information, uncertainty tends to decrease. For instance, reading customer reviews can help us feel more confident about which product to choose. This process of adjusting our beliefs when new evidence appears is explained by a mathematical principle developed by the 18th-century scholar Thomas Bayes. His formula describes how a logical thinker updates decisions when faced with uncertain options.

Using Data to Anticipate Outcomes

By merging these earlier ideas with modern information mathematics, particularly signal processing, researchers gain a powerful method for analyzing social behavior. This approach has already been applied in several fields:

• Financial markets: Understanding how investors react to new information and how that reaction influences stock prices.
• Nature: Observing how plants, such as flowers, interpret sunlight and turn toward it.
• Politics: Estimating the likelihood that a candidate will win an election based on current polling data.

Tracking how information spreads can even help predict how misleading stories or false claims might influence public opinion. One important aspect of Bayesian updating is that every possible option—whether correct or incorrect—can shape how people behave.

Certainty, Beliefs, and Bias

The way our minds react to information often depends on how confident we already feel. When we have no strong prior belief, we tend to consider multiple possibilities more evenly. This represents a state of high uncertainty. On the other hand, if someone strongly believes in one option, new information may have little immediate effect on their viewpoint, creating a stable sense of certainty.

This tendency can lead to confirmation bias, where individuals prefer information that supports their existing beliefs. Although it might appear irrational, mathematical models suggest that it can actually align with Bayesian reasoning: people naturally seek a state where their understanding feels more certain.

Identifying the “Rational Liar”

One of the most intriguing implications of this research is its potential to distinguish between honest mistakes and intentional deception.

• Someone who is mistaken: When a person simply has incorrect information, their beliefs typically move gradually toward the truth as they learn more. Even if they resist change at first, their perspective slowly adjusts over time.
• Someone who is lying: A person who knows the truth but intentionally rejects it behaves differently. They may quickly commit to one false claim and present it confidently. When that claim is disproven, instead of shifting toward the truth, they often switch just as quickly to another incorrect explanation.

Because of this pattern, a person deliberately spreading falsehoods may appear inconsistent or unpredictable, which can help reveal deceptive behavior. Mathematical analysis suggests that such erratic shifts are statistically unlikely to come from simple misunderstanding.

Using this information-based framework, researchers hope to better study how beliefs form and spread—and how society can analyze and respond to the harmful effects of misinformation.